I've been thinking about this question for a while, and I can find evidence for each, I really haven't come to a conclusion. My question is, is music mathematical, following the logical procession between notes; or abstract, being able to materialize the feelings of the author?

SurgicalSteel wrote:Wow, you're spectacularly unhelpful! I think you have a real talent for not being helpful!

Funny thing being, I just read the first Dirk Gently book by Douglas Adams, and it has a wonderful essay written by the main character about mathematics and music that is very much relevant to this thread.

The first four paragraphs are about how music is mathematics, then comes the really interesting part ( which I highlighted, just for you ) about emotion. Point being, music is not abstract or logical, emotional or just calculations, it's both.

Spoiler:

Mathematical analysis and computer modelling are revealing to us that the shapes and processes we encounter in nature -- the way that plants grow, the way that mountains erode or rivers flow, the way that snowflakes or islands achieve their shapes, the way that light plays on a surface, the way the milk folds and spins into your coffee as you stir it, the way that laughter sweeps through a crowd of people -- all these things in their seemingly magical complexity can be described by the interaction of mathematical processes that are, if anything, even more magical in their simplicity. Shapes that we think of as random are in fact the products of complex shifting webs of numbers obeying simple rules. The very word ‘natural’ that we have often taken to mean ‘unstructured’ in fact describes shapes and processes that appear so unfathomably complex that we cannot consciously perceive the simple natural laws at work. They can all be described by numbers.

We know, however, that the mind is capable of understanding these matters in all their complexity and in all their simplicity. A ball flying through the air is responding to the force and direction with which it was thrown, the action of gravity, the friction of the air which it must expend its energy on overcoming, the turbulence of the air around its surface, and the rate and direction of the ball’s spin. And yet, someone who might have difficulty consciously trying to work out what 3 x 4 x 5 comes to would have no trouble in doing differential calculus and a whole host of related calculations so astoundingly fast that they can actually catch a flying ball. People who call this ‘instinct’ are merely giving the phenomenon a name, not explaining anything.

I think that the closest that human beings come to expressing our understanding of these natural complexities is in music. It is the most abstract of the arts -- it has no meaning or purpose other than to be itself.Every single aspect of a piece of music can be represented by numbers. From the organisation of movements in a whole symphony, down through the patterns of pitch and rhythm that make up the melodies and harmonies, the dynamics that shape the performance, all the way down to the timbres of the notes themselves, their harmonics, the way they change over time, in short, all the elements of a noise that distinguish between the sound of one person piping on a piccolo and another one thumping a drum -- all of these things can be expressed by patterns and hierarchies of numbers. And in my experience the more internal relationships there are between the patterns of numbers at different levels of the hierarchy, however complex and subtle those relationships may be, the more satisfying and, well, whole, the music will seem to be.

In fact the more subtle and complex those relationships, and the further they are beyond the grasp of the conscious mind, the more the instinctive part of your mind -- by which I mean that part of your mind that can do differential calculus so astoundingly fast that it will put your hand in the right place to catch a flying ball -- the more that part of your brain revels in it. Music of any complexity (and even ‘Three Blind Mice’ is complex in its way by the time someone has actually performed it on an instrument with its own individual timbre and articulation) passes beyond your conscious mind into the arms of your own private mathematical genius who dwells in your unconscious responding to all the inner complexities and relationships and proportions that we think we know nothing about.

Some people object to such a view of music, saying that if you reduce music to mathematics, where does the emotion come into it? I would say that it’s never been out of it.

The things by which our emotions can be moved -- the shape of a flower or a Grecian urn, the way a baby grows, the way the wind brushes across your face, the way clouds move, their shapes, the way light dances on the water, or daffodils flutter in the breeze, the way in which the person you love moves their head, the way their hair follows that movement, the curve described by the dying fall of the last chord of a piece of music -- all these things can be described by the complex flow of numbers.

That’s not a reduction of it, that’s the beauty of it.Ask Newton.Ask Einstein.Ask the poet (Keats) who said that what the imagination seizes as beauty must be truth. He might also have said that what the hand seizes as a ball must be truth, but he didn’t, because he was a poet and preferred loafing about under trees with a bottle of laudanum and a notebook to playing cricket, but it would have been equally true.

Because that is at the heart of the relationship between on the one hand our ‘instinctive’ understanding of shape, form, movement, light, and on the other hand our emotional responses to them. And that is why I believe that there must be a form of music inherent in nature, in natural objects, in the patterns of natural processes.

A music that would be as deeply satisfying as any naturally occurring beauty -- and our own deepest emotions are, after all, a form of naturally occurring beauty

While the argument is there for both, my own personal opinion, which can be contradicted by anyone else's, is that music is primarily abstract. Our western style of notation is just a way to describe in a mathematical way that we can understand. I myself have played peices that, when listening back to them, just sound like different sounds together. The thing that makes the music is the artist's ability to make a story out of the peice; almost as if whatever your playing, a scale, an etude, or a symphony, was part of a musical and you could hear the lyrics. Both sides of the argument are convincing, but that's just my point of view.

The essay is very interesting, and I like what it has to say, I'll have to look into buying that...

OP, can you define "mathematical" and "abstract"? In my understanding the two are not on the same axis, let alone in some way mutually exclusive so that the question is an either/or situation. I'd say music is both mathematical and abstract, except where it uses concrete sounds or enunciates language.

I have the same doubt as Dream. I have to say one thing, though: as far as our understanding has come, the only way in which music could "materialise" something is through some very powerful form of wizardry, or through divine intervention. Music is inherently immaterial -- it is energy. It can't materialise anything.

It can, though, induce some very powerful feelings inside of us which may or may not be in line with what the artist originally intended. Some music can have a very specific, crystalline, meaning, yet many people still miss the point entirely (there are whole pages in TV Tropes documenting that); some music can be completely devoid of any meaning whatsoever, and many people are still able to associate things with it; some music is meant to be deliberately vague and open to any "meaning", and each person will come up with a personal meaning that's entirely unique.

Music is governed by rules, such as everything must be in the same key, or in the same time, however these are nothing like mathematics, and often these rules can be broken, they are realy just conventions that make it easier for different musicians to work together, not laws of nature.

If you're saying that music could be broken down into numbers like the in Douglas Adams qoute, yes it can and so can everything else in a way, but I don't think that's what the real things are, mathematics is a kind of perfect world, that is a useful kind of diagram of reality but doesn't have the bumps and blemishes and infinitly spiraling complexities of life itself.

If music was mathematical you could expect that it would effect everyone in the same way, but then you might say that everyone is different, so if through some stroke of incredible luck two people were exactly the same, they would be effected in the same way by a piece of music, that's something that's impossible to know.

The test of true mathematics would surely be something that works, that is useful in some way. Maybe one day they will make mathematically or computer generated music that satisfy human taste but I don't think it's likely and I don't think it's soon. Maybe we are too bewitched by illusions of individuality and passion and artistry, or maybe we should realise it's ok for there to be things that we can't explain away such as consciousness, and that it's ok to have on one side science or maths and then also have a whole seperate other thing called art.

limb wrote:Maybe one day they will make mathematically or computer generated music that satisfy human taste but I don't think it's likely and I don't think it's soon.

It's not likely, it's certain, and it's not soon, it's in the past. Serialism is mathematically generated music, and the Music 'N' tradition is computer generated music. Neither is particularly popular, but then neither are lots of musics, so that's not important. They've been around for decades, and while both are a bit archaic in many ways, both still influence music today, and are still used in composition all over the world.

I think music is always abstract because it represents some idea, concepts, sentiments, etc. When music behaves in a predictable pattern of pitches, rhythms, and harmonies, then it's "mathematical". Although argument can be made even when the music doesn't follow a predictable pattern, one can say it's "stochastic" and thus still mathematical.

limb wrote:Maybe one day they will make mathematically or computer generated music that satisfy human taste but I don't think it's likely and I don't think it's soon.

It's not likely, it's certain, and it's not soon, it's in the past. Serialism is mathematically generated music, and the Music 'N' tradition is computer generated music. Neither is particularly popular, but then neither are lots of musics, so that's not important. They've been around for decades, and while both are a bit archaic in many ways, both still influence music today, and are still used in composition all over the world.

I know you could make music mathematically and I am sure people have done so in the past, I remember once reading that Aphex Twin used to write computer programs that generated their own music, or it would be very easy to say spit out paintings according to some random mechanical process, but that isn't what art or music is about. Music is about expression of emotions, I meant a computer that you could talk to and say, "yeah like that but happier, or moodier or whatever" and it would rumble through it's algorithms or whatever and come up with something, which is something all good musicians do instantly when they're jamming and is a lot of what music is about.

Music can be a lot of things anyway, a hundred people could cut it up in a hundred different ways and no one would be any wiser.

limb wrote:Music is about expression of emotions, I meant a computer that you could talk to and say, "yeah like that but happier, or moodier or whatever" and it would rumble through it's algorithms or whatever and come up with something, which is something all good musicians do instantly when they're jamming and is a lot of what music is about.

I think that genereates a strong discussion. I absolutely think that music, and every art, is all about expression, but not necessarily "emotions". Emotions come naturally, whether we want it or not. You can express emotion, but you can express anything else -- but neither of those two possibilities implies that the listener will have any emotions stimulated or not; one can find Autechre's music extremely ressonant, while another thinks John Lennon is a boring arse.

A computer can run algorithms to produce musical piece, but it will be always strictly bounded to how it is programmed, and as of yet, computers are always programmed by humans. So, at its essence, any piece a computer "writes" is actually written by whomener built the computer, without exceptions. This has a lot to do with what Hofstadter talks about in Gödel, Escher, Bach of humans rationalising about what they do while they're doing it, which is something computers can't do. That is composition: you can't compose without thinking about what you're composing, and that's the whole point of it. I don't think that "expressing emotion" is a sine qua non condition of art in the sense that "no emotion = not music", but in the sense that it's impossible to make art devoid of emotion, even when there is a computer in the process.

cjmcjmcjmcjm wrote:Use computers to generate disposable songs for the masses and let humans compose music for those with the ability to appreciate it to enjoy.

Funny. Some people try to erase the line between "erudite" music and "for the masses", while some people try hard to turn that line into an abyss. I'm rather proud to put myself firmly into the former camp.

At risk of sounding shallow, I would say it depends on how good the music is. If it's bubble gum pop, it would be primarily mathematical, because it doesn't have much else to make it special except for its conformance to the tempo, chord spacing, etc. However, the better the song gets, the more it means. If it has a deep emotional background, if the musicians are especially talented and have written crazy syncopation and unique instrumentation, the more the song means more than the musical constraints that it's built on. It's kinda funny, because it seems like it should be the other way (more complexities, more math), but I'd much faster say that Rebecca Black's Friday is stronger in its mathematical compliance than it is in meaning and artistry.

PolakoVoador wrote:Pizza is never a question, pizza is always the answer.

poxic wrote:When we're stuck, flailing, and afraid, that's usually when we're running into the limitations of our old ways of doing things. Something new is being born. Stick around and find out what it is.

Because I was bored I decided to ask this question on Omegle. The result was pretty interesting.

When I asked "I music mathematical or emotional?" most responses went like:

Spoiler:

You're now watching two strangers discuss your question!Question to discuss:Is music mathematical or emotional?Stranger 2: mathematicalStranger 1: good music is emotional

But when I asked "Is music just mathematics or is there more to it?" I got:

Spoiler:

You're now watching two strangers discuss your question!Question to discuss:Is music just mathematical or is there more to it?Stranger 2: More to it, yeah.Stranger 1: noooooStranger 1: dont link music to mathStranger 2: Indeed.Stranger 2: Please don't.Stranger 2: It just makes you sound like a nerd who has no musical talent.Stranger 1: my head'' be spinning with numbersStranger 1: *llStranger 2: You know what kind of people think that art is simply a matter of numbers or cliches?Stranger 2: Tropers.Stranger 2: Do you want to be like one of those fuckers?Stranger 1: hahaStranger 2: I sure wouldn't. But I also don't think there's some mathematical equation to making music.Stranger 1: yesStranger 1: agreedStranger 2: Asker is a fucking TVTropes using neckbeard.Stranger 2: *brofist*Stranger 1: u hear that mr spy?Stranger 1: go n some up with a diff questionStranger 2: Indeed.

Apparently, most people don't like the idea of music as maths. I even dare say; apparently most people don't like maths.

Spoiler:

Interviewer: Some people say they can’t understand your writing even after they read it two or three times. What approach would you suggest for them?

UniqueScreenname wrote:At risk of sounding shallow, I would say it depends on how good the music is. If it's bubble gum pop, it would be primarily mathematical, because it doesn't have much else to make it special except for its conformance to the tempo, chord spacing, etc.

If that were the case, then we wouldn't have some "bubblegum" artists being far more popular than others, and virtually every artist of that kind would be pretty much equally popular; unless you think some companies have better algorithms and heuristics for optimising the "quality" function of their "bubblegum" music, which is a frankly silly and absurd idea.

Marketing is a thing. So is taste, and the inertia of popularity. These adequately explain the popularity of some artists over others without questioning the idea that maybe all the pop music is formulaic to the point of being mathematically explicable.

Also, you've heard of The Neptunes and Timbaland and the like? Some people do actually have better "algorithms", and their studios put out much more popular music than others.

UniqueScreenname wrote:At risk of sounding shallow, I would say it depends on how good the music is. If it's bubble gum pop, it would be primarily mathematical, because it doesn't have much else to make it special except for its conformance to the tempo, chord spacing, etc.

If that were the case, then we wouldn't have some "bubblegum" artists being far more popular than others, and virtually every artist of that kind would be pretty much equally popular; unless you think some companies have better algorithms and heuristics for optimising the "quality" function of their "bubblegum" music, which is a frankly silly and absurd idea.

If popularity was based just on music, that would be true, but it's based on how people react to the people performing it, the way the dress, act, what they say, where they come from, all sorts of stuff. It isn't strictly mathematical.

PolakoVoador wrote:Pizza is never a question, pizza is always the answer.

poxic wrote:When we're stuck, flailing, and afraid, that's usually when we're running into the limitations of our old ways of doing things. Something new is being born. Stick around and find out what it is.

Dream wrote:Marketing is a thing. So is taste, and the inertia of popularity. These adequately explain the popularity of some artists over others without questioning the idea that maybe all the pop music is formulaic to the point of being mathematically explicable.

Actually, they directly question the idea that the quality of music (or, more specifically, the quality of "bubblegum music" -- as if that distinction existed! ) is somehow mathematically defined or calculated. Say, if what UniqueScreenname said about "simple" music being mathematically defined was true, then marketing and promotion would not be a decisive aspect of artists' popularity -- you would only need to show people that a song exists, and the mathematical properties of the song would be enough for people to like it. But if you say that marketing and other things to count, then it's because the mathematical properties are not enough. So, if that's the case, then the mathematical qualities of a song are not enough -- people need to be suggested to like it, and therefore the "mathematics of bubblegum music" are quite complex, because as it happens, sometimes artists are overmarketed to death and people still don't like him, while artists unexplainably become very famous by simple word-of-mouth. You know, that kind of stuff does happen.

What I am suggesting is that those mathematical rules and properties of music do exist and they affect all kinds of music that have ever existed and will ever exist in the world. The thing is, it's not just the properties inherent to the music that matter, because the way people interpret the music are much, much more unimaginably complex! Thus it happens that some people may feel a whole world of emotions when listening to something by Justin Bieber yet feel largely indifferent to Beethoven's 33 Variations on a theme by Diabelli, simply because of many social, cultural, educational factors and so on. And, guess what? Even such a masterpiece by one of the greatest composers in the history of Western music was very largely based on "mathematical" principles that Beethoven may have no realised that were mathematical in the first place. Composers like him knew a lot about harmony, musical structure, melody, dynamics and so on, and knew which rules to follow and which rules to subvert, while some of the "bubbegum" artists may not know a lot about musical theory but they might just feel when something sounds right and when it doesn't sound. Yet, in both cases, the music is still governed by the same rules.

I sustain that mathematics aren't very useful for our need to discard other people's tastes in a way that makes us feel smugly superior. We'll have to recur to other aspects. "Talent", "emotion" and so on may help, but they are a lot more related to our interpretation of music than to the music itself.

The Ancient Greeks often stated that 'music and astronomy are two sides of the same coin'. Astronomy describes relationships between that which is tangible: permanent, external, observable objects, and music describes relationships between invisible, fleeting and hidden objects. This is reflected in the belief in 'the music of the spheres' that is still present in modern music theory, and in the ability of music to be classified in different periods as either part of the trivium or the quadrivivium. So yes, it was seen as both emotional and mathematical, and probably would have stayed this way but for the interference of the Catholic Church, specifically Sts. Augustine and Gregory, who were torn between enjoyment of music and the propriety of the Liturgy. They chose the propriety of the Liturgy and developed plainchant.

Moving forward to approximately the thirteenth century, there was a marked change in the way music was written with the emergence of Le École de Notre Dame de Paris and organum, or the "popularisation" (in the sense of that it spread from Paris to other European centres) and codification (to an extent) of polyphony. Music was seen as a largely mathematical exercise. The composer was not thought of a composer but as a type of divine mathematician who had a magical dove from heaven whispering compositions in his ear. An important but small step away from this was the troubadours and trouvères, who provided music as courtly entertainment and performed mostly secular music. The isorhythmic motet was predominant at the end of this century and the beginning of the next

The fourteenth century saw the emergence of Ars nova and Ars subtilior, both of which shunned the isorhythm and advocated greater rhythmic freedom. However, music still used imitative counterpoint and was very mathematical. However, the concept of composer as creator began to be popularised. Ars nova eventually developed into the chanson française (early 15th century), which then became many different types of regional song (such as the German Lied) as it disseminated across Europe.

Right. So sixteenth century Germany. Middle of the Italian Renaissance, and it's spreading across Europe. Humanism is popular amongst the educated. Martin Luther and the Ninety-Five Theses. BOOM! Reformation. BOOM! Counter-Reformation and the Council of Trent.

It is important to note that music was a main concern of the Council of Trent. The question was, 'how to make good music and transit the text of the Mass/Liturgy clearly (for those who could understand Latin)?'The answer was Palestrina and prima practica,The first generation of music theorists advocating this technique: (includes Tinctoris)• Proper regulation of consonance and dissonance• Every phrase must start and end with perfect intervals (P8, P5, unison)• No chromatic dissonances (ex. m2, TT)• Diatonic dissonances (M2, M7, P4) must appear on the weak beat and be approached and left by step• Melodic motion is conjunct • Leaps must be balanced by motion in the opposite direction• Parallel fifths and octaves are not allowedThe second generation of theorists • Just intonation (predecessor of equal-tempering)• Recognised the supremacy of the triad over the interval for part writing (fuller sound, harks back to le contenance anglois)• First to attempt to explain the mortal sins of parallel fifths and octavesThe third generation expanded on these ideas• Flourid counterpoint (four voices. Getting close to Baroque)• Invertible counterpoint • Transposition of voices in respect to each other• Imitative technique• Contrapuntal procedures such as the cannon

...As well as harmonic progressions that every good (tonal) composer used. Even atonality (and serialism: the bane of many) has very specific mathematical formulæ. Most emotions that are triggered by the most heart-wrenching piece are a condition of its mathematics. For example, String Quartet No 8 by D. Shostakovich. This displays a wide range of emotions, from absolute mania (in the form of a demonic dance) to the deepest depression (adagio). The effect of this is furthered by using chromaticism and really 'crunchy' intervals (tritones galore. Love a tritone. And an Ood. A tritone and an Ood) However, if the demonic dance were to be played at half the tempo, it would be depressing and vice-versa for the adagio. The most abstract aspect of music, emotion, is purely a condition of the math.

Petrucci wrote:The most abstract aspect of music, emotion, is purely a condition of the math.

I really have trouble believing this is true. Yes, there are reliable mathematical relationships that tend to evoke certain responses within certain cultures, but how much is this a result of the mathematical relationship, and how much of it is conditioning towards that particular mathematical relationship?

I've also experienced pretty tremendous emotional responses to music based on factors like texture that are unrelated to the mathematical relationship between notes, or to music that doesn't even have identifiable notes or melodies.

Take a song like, say, Like Gold and Faceted by the band Earth. I find it beautiful and powerful even though it is essentially the same note held at the same volume for 30 minutes, with textural stuff going on in the background. I can't think of any mathematical relationship that would explain my emotional response to this, or to most drone, noise, or ambient music. So how can you say that emotional response is a purely mathematical condition?

Sweeney_Todd wrote:I've been thinking about this question for a while, and I can find evidence for each, I really haven't come to a conclusion. My question is, is music mathematical, following the logical procession between notes

No. There is no system of logic to describe the procession between notes, unless you define "what keys I felt like hitting" or "what notes I felt like writing down" as "logic" which I would as a composer be very pleased to hear a meaningful description of!

; or abstract, being able to materialize the feelings of the author?

Not really, since feelings are pretty simple things. I'm feeling sad, I'm feeling happy, mad, grateful, anxious, etc. Superficially music seems to be just that, a 1:1 correspondence between music and emotion. I.e., I used to think minor keys were "sad" keys and major ones "happy." Of course I was 8 years old at the time. Music of course invokes emotional responses in the listener, and does the same and can be surely inspired by emotions of the performer or composer, but it's unlikely that these are the same thing. There is an entirely subjective quality about it all that makes music hard to pin down as either abstract or mathematical, simple or logical, happy or sad, or whatever.

When it comes to music I tend to think more along the lines of Beethoven, who is quoted as saying, "Music is the one incorporeal entrance into the higher world of knowledge which comprehends mankind but which mankind cannot comprehend."

Petrucci wrote:This displays a wide range of emotions, from absolute mania (in the form of a demonic dance) to the deepest depression (adagio). The effect of this is furthered by using chromaticism and really 'crunchy' intervals (tritones galore. Love a tritone. And an Ood. A tritone and an Ood)

Ooh, what's the mathematical formula for a demonic dance? Be sure to express it in mathematics. In fact, I demand a mathematical proof of demonic dance mania!

You can ask this question to 100 different people and you will get 100 different answers. That is because music is something that, while able to be enjoyed in a group, many find pleasure in alone. It is personal. Music can evoke spiritualism, emotions, memories. Music is solitude and loneliness. Music is love and joy. Music is whatever you make it out to be.

However, there is also a mathematical aspect to music. There are certainly studies that show that people who are proficient in music are more likely to succeed in certain areas, such as math. And there are university classes that tie together math and music. Certainly, to compose music you need to be able to grasp the fundamentals of math. Switching from 7/8 to 5/7 to 4/2 in a matter of a few measures can be tricky for an instrumentalist -- counting is an invaluable tool (rhythm, too), one that the composer must utilize as well. Sadly, most observers will never notice such crazy, wonderful trickery when they listen to the songs played.

Personally, this is a very hard question to answer, mainly because I play six instruments and connect to music in a different way. It used to be my refuge, but as my depression worsened, I abandoned the pursuit of musical pastimes and I began to dread being asked to play.

I believe that music is inherently unknowable, but I don't think that "abstract" is the correct word for it (to me, "abstract," in regard to music, is a substitute for "dissonance" -- but I'm not here to argue over word choice, because that is silly). Music is both mathematical and emotional; music is neither mathematical nor emotional. Music just is. And honestly, I'm not too concerned with whether music is more of one thing or another -- I'm going to just sit back and enjoy it for what it is. Whatever it is.

It's like any art. It can be analyzed however you want to analyze it, and sometimes you'll come away with a logical explanation for why the music makes you feel a certain way, and sometimes you just won't understand it.

I think music can be expressed more mathematically than other forms of art, though. On a basic level, any sound at all can be expressed with a 2 dimensional graph. On a macro level, music can be expressed linearly with notes having defined pitches and lengths. Whereas with something like painting, I'm not sure you can reduce it to numbers as easily. There are many more factors involved. I suppose you could divide the painting into tiny squares and set an RGB value for each pixel. But then why are original paintings worth so much more than prints? (compared with original master tracks vs. high fidelity copies)

The more I thing about it, the more I realize I don't even understand the question. At some level, can mathematics be seen as "abstract"? If you don't think some equations or math concepts are inexplicably beautiful, that probably just means you haven't advanced far enough in math. So what does it mean for something to be "abstract"? I honestly don't know. If it means that something can't be expressed in numbers, then I might say that music is 99% mathematical. But that doesn't mean that it can't be intensely and inexplicably emotional.

At some level, can mathematics be seen as "abstract"? If you don't think some equations or math concepts are inexplicably beautiful, that probably just means you haven't advanced far enough in math. So what does it mean for something to be "abstract"? I honestly don't know. If it means that something can't be expressed in numbers, then I might say that music is 99% mathematical. But that doesn't mean that it can't be intensely and inexplicably emotional.

I always thought mathematics were strictly abstract, as in maths being the abstract patterns and rules behind the things we experience as concrete realities.

Then again, I've never been any good at maths, so it's more than likely that this is wrong.

Spoiler:

Interviewer: Some people say they can’t understand your writing even after they read it two or three times. What approach would you suggest for them?

I think your question is far too generalized to be answerable by a single solid conclusion. Also as was mentioned above Math and the Abstract are not really on the same plane of comparison, both can co-exist in a system or not.

To put my own two cents in, however, I feel as though when I write percussion parts in my band, I tend to break down the song structure mathematically into separate parts. For example, bars 1-5 are to be played in 3/4, while the guitar plays 3 bars of 5/4, which create a 3-5 Poly-rhythm. When constructing music I would say from the percussion and rhythm side specifically music is physically all math. Be it tempo, time-signature, tuplets or whatever else is required; all of it has a pre-determined pattern and very much logic-based.

However on the other hand, when working on melody you're given a lot more freedom to play whatever you want. Although through the circle of fifths you could also argue that it also has a fairly mathematical approach to song writing, especially popular western music. But I would argue melody in comparison to rhythm is far less math and more interpretation and art.

Lastly as many people have mentioned above how one feels as they listen to a specific composition is on another plane of existence when it comes to judging whether or not music is logical or otherwise.

In conclusion I feel as though to get an answer you have to specify exactly what aspect of music you're curious about. Music in general is just too big of a subject.

The other day I was feeling really happy about something so I wrote a little tune that "describes" how I was feeling, in music! That is, when I hear it, it makes me feel that same way that I felt when I wrote it.

Then my friend had this one tune that he wrote but I didn't like the way it modulated, so I used a secondary dominant to make the transition less abrupt.